Simplify Square Root of 87362

Here we will show you two methods that you can use to simplify the square root of 87362. In other words, we will show you how to find the square root of 87362 in its simplest radical form using two different methods.

To be more specific, we have created an illustration below showing what we want to calculate. Our goal is to make "A" outside the radical (√) as large as possible, and "B" inside the radical (√) as small as possible.

√87362 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 87362 to simplify the square root of 87362. This is how to calculate A and B using this method:

A = Calculate the square root of the greatest perfect square from the list of all factors of 87362. The factors of 87362 are 1, 2, 11, 19, 22, 38, 121, 209, 242, 361, 418, 722, 2299, 3971, 4598, 7942, 43681, and 87362. Furthermore, the greatest perfect square on this list is 43681 and the square root of 43681 is 209. Therefore, A equals 209.

B = Calculate 87362 divided by the greatest perfect square from the list of all factors of 87362. We determined above that the greatest perfect square from the list of all factors of 87362 is 43681. Furthermore, 87362 divided by 43681 is 2, therefore B equals 2.

Now we have A and B and can get our answer to 87362 in its simplest radical form as follows:

√87362 = A√B

√87362 = 209√2

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 87362 to simplify the square root of 87362 to its simplest form possible. This is how to calculate A and B using this method:

A = Multiply all the double prime factors (pairs) of 87362 and then take the square root of that product. The prime factors that multiply together to make 87362 are 2 x 11 x 11 x 19 x 19. When we strip out the pairs only, we get 11 x 11 x 19 x 19 = 43681 and the square root of 43681 is 209. Therefore, A equals 209.

B = Divide 87362 by the number (A) squared. 209 squared is 43681 and 87362 divided by 43681 is 2. Therefore, B equals 2.

Once again we have A and B and can get our answer to 87362 in its simplest radical form as follows:

√87362 = A√B

√87362 = 209√2

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Simplify Square Root of 87363
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